Question: Simplify the following expression: $ k = \dfrac{3}{p + 5} + \dfrac{-10}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{3}{p + 5} \times \dfrac{7}{7} = \dfrac{21}{7p + 35} $ Multiply the second expression by $\dfrac{p + 5}{p + 5}$ $ \dfrac{-10}{7} \times \dfrac{p + 5}{p + 5} = \dfrac{-10p - 50}{7p + 35} $ Therefore $ k = \dfrac{21}{7p + 35} + \dfrac{-10p - 50}{7p + 35} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{21 - 10p - 50}{7p + 35} $ $k = \dfrac{-10p - 29}{7p + 35}$